{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SEDNXGM5WQVFHVVTZUXFNQ6M3S","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"4e0680c3051c3b2e1bdee87b2349bd44c05fd4fddbebab168c37fc20102dedaa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-09-17T20:50:41Z","title_canon_sha256":"64c22bfb865d4025a63c9708f57e30f0c6e827bedc4e72d6eb7b0380ac663459"},"schema_version":"1.0","source":{"id":"1609.05387","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.05387","created_at":"2026-05-18T00:55:51Z"},{"alias_kind":"arxiv_version","alias_value":"1609.05387v3","created_at":"2026-05-18T00:55:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.05387","created_at":"2026-05-18T00:55:51Z"},{"alias_kind":"pith_short_12","alias_value":"SEDNXGM5WQVF","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SEDNXGM5WQVFHVVT","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SEDNXGM5","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:4f043050d5d8b83265bb2c3272fb15b196420a4403a5f994457a4cb0b9633301","target":"graph","created_at":"2026-05-18T00:55:51Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, we study the spreading speeds and traveling wave solutions of the PDE $$ \\begin{cases} u_{t}= \\Delta u-\\chi \\nabla \\cdot (u \\nabla v) + u(1-u),\\ \\ x\\in\\mathbb{R}^N 0=\\Delta v-v+u, \\ \\ x\\in\\mathbb{R}^N, \\end{cases} $$ where $u(x,t)$ and $v(x,t)$ represent the population and the chemoattractant densities, respectively, and $\\chi$ is the chemotaxis sensitivity. It has been shown in an earlier work by the authors of the current paper that, when $0<\\chi<1$, for every nonnegative uniformly continuous and bounded function $u_0(x)$, the system has a unique globally bounded classical sol","authors_text":"Rachidi Salako, Wenxian Shen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-09-17T20:50:41Z","title":"Spreading Speeds and Traveling waves of a parabolic-elliptic chemotaxis system with logistic source on R^N"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.05387","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f5b91ee46e5957f7f08058ca9e5ca8c73e413372e51cf913c8b325618350856f","target":"record","created_at":"2026-05-18T00:55:51Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"4e0680c3051c3b2e1bdee87b2349bd44c05fd4fddbebab168c37fc20102dedaa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-09-17T20:50:41Z","title_canon_sha256":"64c22bfb865d4025a63c9708f57e30f0c6e827bedc4e72d6eb7b0380ac663459"},"schema_version":"1.0","source":{"id":"1609.05387","kind":"arxiv","version":3}},"canonical_sha256":"9106db999db42a53d6b3cd2e56c3ccdc93dc3d9dcdd98c54c331809dde79c257","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9106db999db42a53d6b3cd2e56c3ccdc93dc3d9dcdd98c54c331809dde79c257","first_computed_at":"2026-05-18T00:55:51.713490Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:51.713490Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"szd12fqftVUTA10I73wcK4ZDAuZEGUwCjS5lEyOSI/QxmT1epOeiZsH2WldDPCjVXovWHN7r4jPtAzT/H+XtAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:51.714023Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.05387","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f5b91ee46e5957f7f08058ca9e5ca8c73e413372e51cf913c8b325618350856f","sha256:4f043050d5d8b83265bb2c3272fb15b196420a4403a5f994457a4cb0b9633301"],"state_sha256":"71626058895cd2c3302fc205be12aa3c5a443be81b429d1ee349cd7cb4d04d01"}